BIOL2007- POPULATION GENETICS
TUTORIAL - Single locus selection and drift
Due: Friday 25 January, 4:30pm,
in Wolfson House 306 coursework box
Use lecture handouts when
necessary. Ring tutor or J. Mallet when all else fails!
1) In a study of the
peppered moth in Central Birmingham in 1954, the following genotype
frequencies were found:
carbonaria heterozygotes typica
of heterozygotes were obtained by crossing the CC and Cc x
typica, and looking at progeny ratios).
a) Estimate the
at the C locus, and then, using the Hardy-Weinberg law, find the
b) Use these frequencies
to estimate the expected numbers of genotypes (which should not
be rounded to whole numbers!),
and test for deviation from Hardy-Weinberg using a chi-square goodness of fit
test [Note: , where O=observed numbers,
E=expected numbers]; what is the total chi-square value?
c) Look up the probability
of getting results this extreme in the following simplified chi-square
(Note: for a worked example and problems with degrees of freedom,
see the lecture on "Evolution of Genetic Diversity"). Write down this
d) Is there evidence for deviation
from Hardy-Weinberg? Write down three possible causes for a deviation (whether
there is or isn't).
of Value of
0.99 0.9 0.5 0.1 0.05
0.00 0.02 0.46 2.71 3.84 6.63 10.83
0.02 0.21 1.39 4.61 5.99 9.21 13.82
e) How many C, and how many c alleles were present
in the 1954 sample? How many C+c alleles in total?
2) In 1955 the
population was resampled and the following data were obtained:
c Total alleles
1954 890 148
1955 778 110
Totals 1668 258
a) Perform a chi-square 2x2 test of homogeneity for allele frequency,
to see whether there is any evidence for allele frequency change. Explanation:
The expected values are given by assuming that the gene frequencies have not changed
between years. For example, the expected number of C alleles in 1954 is
given by a combination of the marginal totals: 1038x1668/1926
= 898.9533. The degrees of freedom for homogeneity
tests are given by the formula (r-1)(c-1) where r and c are the numbers of rows
and of columns, here (2-1)(2-1) = 1 degree of freedom. Obtain chi-square value
as in formula above (Note: you may use
Yates' correction if you want, but I will not take marks
off for not doing so. Opinions differ as to whether Yates' correction is sensible).
b) What is the chi-square value? (It should be a sum of four numbers).
c) Look up the value of chi-square on the above table. What is the value
d) What were the allele frequencies? Has there been a significant change in allele
e) What has the change in gene frequency, , been?
f) Given that there is only one generation per year in this species, what is the
selection pressure, s? Use the
formula forgiven in the lecture on single-gene
selection. [HINT: if s seems unreasonable,
and you have checked your arithmetic, don't worry].
3) There has been a controversy about Bernard Kettlewell's mark-release-recapture
experiments. The main controversy is over whether there is evidence for selection
due to predation of moths on polluted and unpolluted backgrounds, or whether there
is some other cause. Here are four brief book reviews on the controversy (you
will need your UCL computer ID and password to download these files; if you don't
have one, ask a friend to do it for you, or go directly to the journals):
Anti visual predation: Coyne,JA (1998):
Not black and white. Review of "Melanism: Evolution in Action" by Michael
E.N. Majerus. Nature 396, 35-36, and Coyne,JA (2002): Evolution under pressure.
Review of Judith Hooper: "Of Moths and Men: Intrigue, Tragedy and the Peppered
Moth. Nature 418, 19-20.
Pro visual predation: Grant,BS (2002): Sour
grapes of Wrath. Review of "Of Moths and Men" by Judith Hooper. Science 297, 940-941.
Neutral: Shapiro,AM (2002): Paint
it black. Review of "Of Moths and Men" by Judith Hooper. Evolution 56, 1885-1886.
News article: Proffitt,F (2004): In defense
of Darwin and a former icon of evolution. Science 304, 1892-1895.
a) Based on these brief reviews, what are your thoughts on this controversy (write
not more than a paragraph or so)?
b) Do you feel any further experiments are needed. If so, what?
c) On the basis of this evidence, vote for or against the idea that visual bird
predation is a cause of the evolution of melanism in the peppered moth, and its
decline since the Clean Air Acts (part (c) will not carry any marks; it is just
to assess public opinion!).
4) a) Inbreeding causes a deficit of heterozygotes
in the population (see "Inbreeding and Neutral Evolution lecture"). Supposing
the numbers of genotypes in an inbred population are: AA 432, Aa 702, aa 1281.
What is the value for F? HINT:Observed heterozygote frequency = 2pq(1-F).
Rearrange to solve for F.
I have a son Kevin, who marrys Cath, and has a daughter, Bertha. However, Cath's
dad, Fred, is in fact her mother's first cousin and also my own first cousin (see
b) What is Bertha's
inbreeding coefficient, F i.e. the probability that she
has an allele at any locus that is identical by descent through my
Hint: add up the probabilities for any paths that go through both of
parents (Kev AND Cath). HINT: You should get only four paths.
c) Is it a bad thing to